Electrical and Electronic Engineering - Research Publications
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ItemInput-to-state stability for a class of hybrid dynamical systems via averaging(Springer, 2012-02)Input-to-state stability (ISS) properties for a class of time-varying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the time-varying hybrid systems with time-invariant hybrid systems. Closeness of solutions between the time-varying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semi-global practical (SGP)-ISS of the actual system. In a similar fashion, ISS of the weak average implies semi-global practical derivative ISS (SGP-DISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulse-width modulated control systems.
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ItemAnalysis for a class of singularly perturbed hybrid systems via averaging(PERGAMON-ELSEVIER SCIENCE LTD, 2012-06-01)A class of singularly perturbed hybrid dynamical systems is analyzed. The fast states are restricted to a compact set a priori. The continuous-time boundary layer dynamics produce solutions that are assumed to generate a well-defined average vector field for the slow dynamics. This average, the projection of the jump map in the direction of the slow states, and flow and jump sets from the original dynamics define the reduced, or average, hybrid dynamical system. Assumptions about the average system lead to conclusions about the original, higher-dimensional system. For example, forward pre-completeness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains. In addition, global asymptotic stability for the average system implies semiglobal, practical asymptotic stability for the original system. We give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems. We also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuous-time plants implemented by fast but continuous actuators.
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ItemPath Following for Nonlinear Systems With Unstable Zero Dynamics: An Averaging Solution(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2011-04-01)We consider a path-following problem in which the goal is to ensure that the error between the system output and the geometric path is asymptotically less than a prespecified constant, while guaranteeing a forward motion along the path and boundedness of all states. Comparing with the results on this problem, we exploit averaging techniques to develop an alternative simpler solution for a class of nonlinear systems and for paths satisfying a certain geometric condition.
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ItemInput-to-state stability analysis via averaging for parameterized discrete-time systems(Watam Press, 2010-12-15)The paper studies semi-global practical input-to-state stability (SGP-ISS) of a parameterized family of discrete-time systems that may arise when an approximate discrete-time model of a sampled-data system with disturbances is used for controller design. It is shown under appropriate conditions that if the solutions of the time varying family of discrete-time systems with disturbances converge uniformly on compact time intervals to the solutions of the average family of discrete-time systems, then ISS of the average family of systems implies SGP-ISS of the original family of systems. A trajectory based approach is utilized to establish the main result.
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ItemInput-to-State Stability and Averaging of Linear Fast Switching Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2010-05-01)We consider the averaging method for stability of rapidly switching linear systems with disturbances. We show that the notions of strong and weak averages proposed in [1], with partial strong average defined in this note, play an important role in the context of switched systems. Using these notions of average, we show that exponential input-to-state stability (ISS) of the strong and the partial strong average system with linear gain imply exponential ISS with linear gain of the actual system. Similarly, exponential ISS of the weak average guarantees an appropriate exponential derivative ISS (DISS) property for the actual system. Moreover, using the Lyapunov method, we show that linear ISS gains of the actual system and its average converge to each other as the switching rate is increased.
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ItemEmulation-based stabilization of networked control systems implemented on FlexRay(PERGAMON-ELSEVIER SCIENCE LTD, 2015-09)Abstract We investigate the emulation controller design approach for nonlinear networked control systems (NCS) with FlexRay. FlexRay is a deterministic communication protocol which is increasingly used in the automotive industry as it provides a high bandwidth and allows for safety critical applications. It is characterized by pre-set communication cycles that are subdivided into static and dynamic segments; the data transmissions are scheduled by different rules depending on the segment. We propose for the first time a hybrid model of NCS with FlexRay for this purpose. We show, under reasonable assumptions, that the asymptotic stability property ensured by the controller in the absence of communication constraints is preserved when the latter is implemented over FlexRay with sufficiently frequent data transmission. In particular, we assume that on each communication segment, the data transmissions are governed by uniformly globally exponentially stable protocols. This covers the case when the round-robin protocol is implemented on the static segment and the try-once-discard protocol is implemented on the dynamic segment. We provide explicit maximum allowable transmission interval bounds that guarantee stability.
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ItemObserver design for networked control systems with FlexRay(PERGAMON-ELSEVIER SCIENCE LTD, 2017-08)We design state observers for nonlinear networked control systems (NCS) implemented over FlexRay. FlexRay is a communication protocol used in the automotive industry, which has the feature to switch between two scheduling rules during its communication cycles. These switches induce technical difficulties when modeling, designing and analyzing observers for such systems compared to standard NCS. We present a solution based on the emulation approach. Given an observer in the absence of communication constraints, we implement it over the network and we provide sufficient conditions on the latter, to preserve the stability property of the observer. In particular, we provide explicit bounds on the maximal allowable transmission intervals, which adapt to the lengths of the segment associated to each scheduling rule. We assume that the plant dynamics and measurements are affected by noise and we guarantee an input-to-state stability property for the corresponding estimation error system. The overall system is modeled as a hybrid system and the analysis relies on the use of a novel hybrid Lyapunov function.
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ItemPeriodic Event-Triggered Control for Nonlinear Networked Control Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2020-02-01)Periodic event-triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input-to-state stability and $\mathcal {L}_p$ stability for the overall system based on a continuous-time output-feedback controller that robustly stabilizes the network-free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.